All the possible values of k will have a pair of one negative and one positive integer except for -24 and -25. So when u add all of them -24 and -25 will remain as they don't have a corresponding positive Hence, -49
U can also list down all numbers
Numbers betn 0 and -26
-(1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 21 23 24 25)
Numbers betn 0 and 24
(1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23)
-24 and -25 remain as it is. Hence D
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Number Problem!!
Source: Beat The GMAT — Problem Solving |
This is time to not panic and be methodical - the GMAT will not ask you to do such a crazy sum. questions about inequalities that span zero are often about the relationship with zero. start thinking how the numbers relate.
the first negative integer will be -25,-24, -23, -22 (ok so we see how that is going to go)
Now look at the positive integers the first will be 23, then 22, 21 .... and hopefully you will notice the pattern that 23-23= 0 and that will happen as you move toward zero. only -25 and -24 are left without positive partners so if you add them you get - 49.
the first negative integer will be -25,-24, -23, -22 (ok so we see how that is going to go)
Now look at the positive integers the first will be 23, then 22, 21 .... and hopefully you will notice the pattern that 23-23= 0 and that will happen as you move toward zero. only -25 and -24 are left without positive partners so if you add them you get - 49.
Becky
Master GMAT Instructor
The Princeton Review
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Master GMAT Instructor
The Princeton Review
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Also, it's not that crazy of a sum to add up if you wanted to:
Number of terms:
25 negatives, 1 zero, 23 positives = 49
Average of terms: (-25 + 23)/2 = -2/2 = -1
Sum = Number of terms * Average = 49 * -1 = -49
Number of terms:
25 negatives, 1 zero, 23 positives = 49
Average of terms: (-25 + 23)/2 = -2/2 = -1
Sum = Number of terms * Average = 49 * -1 = -49
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GMAT Boost offers 250+ challenging GMAT Math practice questions, each with a thorough video explanation, and 100+ GMAT Math video tips, each 90 seconds or less.
It's a total of 20+ hours of expert instruction for an introductory price of just $10.
View sample questions and tips without signing up, or sign up now for full access.
Also, check out the most useful GMAT Math blog on the internet here.
